Predictions — predictions • marginaleffects

Outcome predicted by a fitted model on a specified scale for a given combination of values of the predictor variables, such as their observed values, their means, or factor levels (a.k.a. "reference grid").

predictions(): unit-level (conditional) estimates.
avg_predictions(): average (marginal) estimates.

The newdata argument and the datagrid() function can be used to control where statistics are evaluated in the predictor space: "at observed values", "at the mean", "at representative values", etc.

See the predictions vignette and package website for worked examples and case studies:

Usage

predictions(
  model,
  newdata = NULL,
  variables = NULL,
  vcov = TRUE,
  conf_level = 0.95,
  type = NULL,
  by = FALSE,
  byfun = NULL,
  wts = NULL,
  transform_post = NULL,
  hypothesis = NULL,
  df = Inf,
  ...
)

avg_predictions(
  model,
  newdata = NULL,
  variables = NULL,
  vcov = TRUE,
  conf_level = 0.95,
  type = NULL,
  by = TRUE,
  byfun = NULL,
  wts = NULL,
  transform_post = NULL,
  hypothesis = NULL,
  df = Inf,
  ...
)

Arguments

model

Model object

newdata

NULL, data frame, string, or datagrid() call. Determines the predictor values for which to compute slopes.

NULL (default): Unit-level slopes each observed value in the original dataset.
data frame: Unit-level slopes for each row of the newdata data frame.
datagrid() call to specify a custom grid of regressors. For example:
- newdata = datagrid(cyl = c(4, 6)): cyl variable equal to 4 and 6 and other regressors fixed at their means or modes.
- See the Examples section and the datagrid() documentation.
string:
- "mean": Marginal Effects at the Mean. Slopes when each predictor is held at its mean or mode.
- "median": Marginal Effects at the Median. Slopes when each predictor is held at its median or mode.
- "marginalmeans": Marginal Effects at Marginal Means. See Details section below.
- "tukey": Marginal Effects at Tukey's 5 numbers.
- "grid": Marginal Effects on a grid of representative numbers (Tukey's 5 numbers and unique values of categorical predictors).

variables

NULL, character vector, or named list. The subset of variables to use for creating a counterfactual grid of predictions. The entire dataset replicated for each unique combination of the variables in this list. See the Examples section below.

Warning: This can use a lot of memory if there are many variables and values, and when the dataset is large.
NULL: computes one prediction per row of newdata
Named list: names identify the subset of variables of interest and their values. For numeric variables, the variables argument supports functions and string shortcuts:
- A function which returns a numeric value
- Numeric vector: Contrast between the 2nd element and the 1st element of the x vector.
- "iqr": Contrast across the interquartile range of the regressor.
- "sd": Contrast across one standard deviation around the regressor mean.
- "2sd": Contrast across two standard deviations around the regressor mean.
- "minmax": Contrast between the maximum and the minimum values of the regressor.
- "threenum": mean and 1 standard deviation on both sides
- "fivenum": Tukey's five numbers #' @param newdata NULL, data frame, string, or datagrid() call. Determines the grid of predictors on which we make predictions.

NULL (default): Predictions for each observed value in the original dataset.
data frame: Predictions for each row of the newdata data frame.
string:
- "mean": Predictions at the Mean. Predictions when each predictor is held at its mean or mode.
- "median": Predictions at the Median. Predictions when each predictor is held at its median or mode.
- "marginalmeans": Predictions at Marginal Means. See Details section below.
- "tukey": Predictions at Tukey's 5 numbers.
- "grid": Predictions on a grid of representative numbers (Tukey's 5 numbers and unique values of categorical predictors).
datagrid() call to specify a custom grid of regressors. For example:
- newdata = datagrid(cyl = c(4, 6)): cyl variable equal to 4 and 6 and other regressors fixed at their means or modes.
- See the Examples section and the datagrid() documentation.

vcov

Type of uncertainty estimates to report (e.g., for robust standard errors). Acceptable values:

FALSE: Do not compute standard errors. This can speed up computation considerably.
TRUE: Unit-level standard errors using the default vcov(model) variance-covariance matrix.
String which indicates the kind of uncertainty estimates to return.
- Heteroskedasticity-consistent: "HC", "HC0", "HC1", "HC2", "HC3", "HC4", "HC4m", "HC5". See ?sandwich::vcovHC
- Heteroskedasticity and autocorrelation consistent: "HAC"
- Mixed-Models degrees of freedom: "satterthwaite", "kenward-roger"
- Other: "NeweyWest", "KernHAC", "OPG". See the sandwich package documentation.
One-sided formula which indicates the name of cluster variables (e.g., ~unit_id). This formula is passed to the cluster argument of the sandwich::vcovCL function.
Square covariance matrix
Function which returns a covariance matrix (e.g., stats::vcov(model))

conf_level

numeric value between 0 and 1. Confidence level to use to build a confidence interval.

type

string indicates the type (scale) of the predictions used to compute contrasts or slopes. This can differ based on the model type, but will typically be a string such as: "response", "link", "probs", or "zero". When an unsupported string is entered, the model-specific list of acceptable values is returned in an error message. When type is NULL, the default value is used. This default is the first model-related row in the marginaleffects:::type_dictionary dataframe.

by

Aggregate unit-level estimates (aka, marginalize, average over). Valid inputs:

FALSE: return the original unit-level estimates.
TRUE: aggregate estimates for each term.
Character vector of column names in newdata or in the data frame produced by calling the function without the by argument.
Data frame with a by column of group labels, and merging columns shared by newdata or the data frame produced by calling the same function without the by argument.
See examples below.

byfun

A function such as mean() or sum() used to aggregate estimates within the subgroups defined by the by argument. NULL uses the mean() function. Must accept a numeric vector and return a single numeric value. This is sometimes used to take the sum or mean of predicted probabilities across outcome or predictor levels. See examples section.

wts

string or numeric: weights to use when computing average contrasts or slopes. These weights only affect the averaging in avg_*() or with the by argument, and not the unit-level estimates themselves.

string: column name of the weights variable in newdata. When supplying a column name to wts, it is recommended to supply the original data (including the weights variable) explicitly to newdata.
numeric: vector of length equal to the number of rows in the original data or in newdata (if supplied).

transform_post

(experimental) A function applied to unit-level adjusted predictions and confidence intervals just before the function returns results. For bayesian models, this function is applied to individual draws from the posterior distribution, before computing summaries.

hypothesis

specify a hypothesis test or custom contrast using a numeric value, vector, or matrix, a string, or a string formula.

Numeric:
- Single value: the null hypothesis used in the computation of Z and p (before applying transform_post).
- Vector: Weights to compute a linear combination of (custom contrast between) estimates. Length equal to the number of rows generated by the same function call, but without the hypothesis argument.
- Matrix: Each column is a vector of weights, as describe above, used to compute a distinct linear combination of (contrast between) estimates. The column names of the matrix are used as labels in the output.
String formula to specify linear or non-linear hypothesis tests. If the term column uniquely identifies rows, terms can be used in the formula. Otherwise, use b1, b2, etc. to identify the position of each parameter. Examples:
- hp = drat
- hp + drat = 12
- b1 + b2 + b3 = 0
String:
- "pairwise": pairwise differences between estimates in each row.
- "reference": differences between the estimates in each row and the estimate in the first row.
- "sequential": difference between an estimate and the estimate in the next row.
- "revpairwise", "revreference", "revsequential": inverse of the corresponding hypotheses, as described above.
See the Examples section below and the vignette: https://vincentarelbundock.github.io/marginaleffects/articles/hypothesis.html

df

Degrees of freedom used to compute p values and confidence intervals. A single numeric value between 1 and Inf. When df is Inf, the normal distribution is used. When df is finite, the t distribution is used. See insight::get_df for a convenient function to extract degrees of freedom. Ex: slopes(model, df = insight::get_df(model))

...

Additional arguments are passed to the predict() method supplied by the modeling package.These arguments are particularly useful for mixed-effects or bayesian models (see the online vignettes on the marginaleffects website). Available arguments can vary from model to model, depending on the range of supported arguments by each modeling package. See the "Model-Specific Arguments" section of the ?marginaleffects documentation for a non-exhaustive list of available arguments.

Value

A data.frame with one row per observation and several columns:

rowid: row number of the newdata data frame
type: prediction type, as defined by the type argument
group: (optional) value of the grouped outcome (e.g., categorical outcome models)
estimate: predicted outcome
std.error: standard errors computed by the insight::get_predicted function or, if unavailable, via marginaleffects delta method functionality.
conf.low: lower bound of the confidence interval (or equal-tailed interval for bayesian models)
conf.high: upper bound of the confidence interval (or equal-tailed interval for bayesian models)

Details

The newdata argument, the tidy() function, and datagrid() function can be used to control the kind of predictions to report:

Average Predictions
Predictions at the Mean
Predictions at User-Specified values (aka Predictions at Representative values).

When possible, predictions() delegates the computation of confidence intervals to the insight::get_predicted() function, which uses back transformation to produce adequate confidence intervals on the scale specified by the type argument. When this is not possible, predictions() uses the Delta Method to compute standard errors around adjusted predictions, and builds symmetric confidence intervals. These naive symmetric intervals may not always be appropriate. For instance, they may stretch beyond the bounds of a binary response variables.

Functions

avg_predictions(): Average predictions

Model-Specific Arguments

Some model types allow model-specific arguments to modify the nature of marginal effects, predictions, marginal means, and contrasts.

Package	Class	Argument	Documentation
`brms`	`brmsfit`	`ndraws`	brms::posterior_predict
		`re_formula`
`lme4`	`merMod`	`include_random`	insight::get_predicted
		`re.form`	lme4::predict.merMod
		`allow.new.levels`	lme4::predict.merMod
`glmmTMB`	`glmmTMB`	`re.form`	glmmTMB::predict.glmmTMB
		`allow.new.levels`	glmmTMB::predict.glmmTMB
		`zitype`	glmmTMB::predict.glmmTMB
`mgcv`	`bam`	`exclude`	mgcv::predict.bam
`robustlmm`	`rlmerMod`	`re.form`	robustlmm::predict.rlmerMod
		`allow.new.levels`	robustlmm::predict.rlmerMod

Bayesian posterior summaries

By default, credible intervals in bayesian models are built as equal-tailed intervals. This can be changed to a highest density interval by setting a global option:

options("marginaleffects_posterior_interval" = "eti")

options("marginaleffects_posterior_interval" = "hdi")

By default, the center of the posterior distribution in bayesian models is identified by the median. Users can use a different summary function by setting a global option:

options("marginaleffects_posterior_center" = "mean")

options("marginaleffects_posterior_center" = "median")

When estimates are averaged using the by argument, the tidy() function, or the summary() function, the posterior distribution is marginalized twice over. First, we take the average across units but within each iteration of the MCMC chain, according to what the user requested in by argument or tidy()/summary() functions. Then, we identify the center of the resulting posterior using the function supplied to the "marginaleffects_posterior_center" option (the median by default).

Examples

# Adjusted Prediction for every row of the original dataset
mod <- lm(mpg ~ hp + factor(cyl), data = mtcars)
pred <- predictions(mod)
head(pred)
#> 
#>  Estimate Std. Error     z   Pr(>|z|) 2.5 % 97.5 %
#>     20.04     1.2041 16.64 < 2.22e-16 17.68  22.40
#>     20.04     1.2041 16.64 < 2.22e-16 17.68  22.40
#>     26.41     0.9620 27.46 < 2.22e-16 24.53  28.30
#>     20.04     1.2041 16.64 < 2.22e-16 17.68  22.40
#>     15.92     0.9925 16.04 < 2.22e-16 13.98  17.87
#>     20.16     1.2186 16.54 < 2.22e-16 17.77  22.55
#> 
#> Prediction type:  response 
#> Columns: rowid, type, estimate, std.error, statistic, p.value, conf.low, conf.high, mpg, cyl, disp, hp, drat, wt, qsec, vs, am, gear, carb 
#> 

# Adjusted Predictions at User-Specified Values of the Regressors
predictions(mod, newdata = datagrid(hp = c(100, 120), cyl = 4))
#> 
#>  Estimate Std. Error     z   Pr(>|z|) 2.5 % 97.5 %  hp cyl
#>     26.25     0.9856 26.63 < 2.22e-16 24.31  28.18 100   4
#>     25.77     1.1096 23.22 < 2.22e-16 23.59  27.94 120   4
#> 
#> Prediction type:  response 
#> Columns: rowid, type, estimate, std.error, statistic, p.value, conf.low, conf.high, mpg, hp, cyl 
#> 

m <- lm(mpg ~ hp + drat + factor(cyl) + factor(am), data = mtcars)
predictions(m, newdata = datagrid(FUN_factor = unique, FUN_numeric = median))
#> 
#>  Estimate Std. Error     z   Pr(>|z|) 2.5 % 97.5 %
#>     21.95      1.288 17.04 < 2.22e-16 19.43  24.48
#>     18.19      1.271 14.31 < 2.22e-16 15.70  20.68
#>     25.55      1.322 19.32 < 2.22e-16 22.96  28.14
#>     21.78      1.541 14.13 < 2.22e-16 18.76  24.81
#>     22.62      2.141 10.56 < 2.22e-16 18.42  26.81
#>     18.85      1.734 10.87 < 2.22e-16 15.45  22.25
#> 
#> Prediction type:  response 
#> Columns: rowid, type, estimate, std.error, statistic, p.value, conf.low, conf.high, mpg, hp, drat, cyl, am 
#> 

# Average Adjusted Predictions (AAP)
library(dplyr)
mod <- lm(mpg ~ hp * am * vs, mtcars)

avg_predictions(mod)
#> 
#>  Estimate Std. Error     z   Pr(>|z|) 2.5 % 97.5 %
#>     20.09     0.4844 41.47 < 2.22e-16 19.14  21.04
#> 
#> Prediction type:  response 
#> Columns: type, estimate, std.error, statistic, p.value, conf.low, conf.high 
#> 

predictions(mod, by = "am")
#> 
#>  am Estimate Std. Error     z   Pr(>|z|) 2.5 % 97.5 %
#>   1    24.39     0.7601 32.09 < 2.22e-16 22.90  25.88
#>   0    17.15     0.6287 27.27 < 2.22e-16 15.92  18.38
#> 
#> Prediction type:  response 
#> Columns: type, am, estimate, std.error, statistic, p.value, conf.low, conf.high 
#> 

# Conditional Adjusted Predictions
plot_predictions(mod, condition = "hp")


# Counterfactual predictions with the `variables` argument
# the `mtcars` dataset has 32 rows

mod <- lm(mpg ~ hp + am, data = mtcars)
p <- predictions(mod)
head(p)
#> 
#>  Estimate Std. Error     z   Pr(>|z|) 2.5 % 97.5 %
#>     25.38     0.8176 31.05 < 2.22e-16 23.78  26.99
#>     25.38     0.8176 31.05 < 2.22e-16 23.78  26.99
#>     26.39     0.8496 31.06 < 2.22e-16 24.72  28.05
#>     20.11     0.7755 25.93 < 2.22e-16 18.59  21.63
#>     16.28     0.6774 24.03 < 2.22e-16 14.95  17.61
#>     20.40     0.7962 25.62 < 2.22e-16 18.84  21.96
#> 
#> Prediction type:  response 
#> Columns: rowid, type, estimate, std.error, statistic, p.value, conf.low, conf.high, mpg, cyl, disp, hp, drat, wt, qsec, vs, am, gear, carb 
#> 
nrow(p)
#> [1] 32

# counterfactual predictions obtained by replicating the entire for different
# values of the predictors
p <- predictions(mod, variables = list(hp = c(90, 110)))
nrow(p)
#> [1] 64


# hypothesis test: is the prediction in the 1st row equal to the prediction in the 2nd row
mod <- lm(mpg ~ wt + drat, data = mtcars)

predictions(
    mod,
    newdata = datagrid(wt = 2:3),
    hypothesis = "b1 = b2")
#> 
#>   Term Estimate Std. Error     z   Pr(>|z|) 2.5 % 97.5 %
#>  b1=b2    4.783      0.797 6.001 1.9629e-09 3.221  6.345
#> 
#> Prediction type:  response 
#> Columns: type, term, estimate, std.error, statistic, p.value, conf.low, conf.high 
#> 

# same hypothesis test using row indices
predictions(
    mod,
    newdata = datagrid(wt = 2:3),
    hypothesis = "b1 - b2 = 0")
#> 
#>     Term Estimate Std. Error     z   Pr(>|z|) 2.5 % 97.5 %
#>  b1-b2=0    4.783      0.797 6.001 1.9629e-09 3.221  6.345
#> 
#> Prediction type:  response 
#> Columns: type, term, estimate, std.error, statistic, p.value, conf.low, conf.high 
#> 

# same hypothesis test using numeric vector of weights
predictions(
    mod,
    newdata = datagrid(wt = 2:3),
    hypothesis = c(1, -1))
#> 
#>    Term Estimate Std. Error     z   Pr(>|z|) 2.5 % 97.5 %
#>  custom    4.783      0.797 6.001 1.9629e-09 3.221  6.345
#> 
#> Prediction type:  response 
#> Columns: type, term, estimate, std.error, statistic, p.value, conf.low, conf.high 
#> 

# two custom contrasts using a matrix of weights
lc <- matrix(c(
    1, -1,
    2, 3),
    ncol = 2)
predictions(
    mod,
    newdata = datagrid(wt = 2:3),
    hypothesis = lc)
#> 
#>    Term Estimate Std. Error      z   Pr(>|z|)   2.5 %  97.5 %
#>  custom    4.783      0.797  6.001 1.9629e-09   3.221   6.345
#>  custom  115.214      3.647 31.587 < 2.22e-16 108.065 122.363
#> 
#> Prediction type:  response 
#> Columns: rowid, type, term, estimate, std.error, statistic, p.value, conf.low, conf.high 
#> 


# `by` argument
mod <- lm(mpg ~ hp * am * vs, data = mtcars)
predictions(mod, by = c("am", "vs")) 
#> 
#>  am vs Estimate Std. Error     z   Pr(>|z|) 2.5 % 97.5 %
#>   1  0    19.75     1.1188 17.65 < 2.22e-16 17.56  21.94
#>   1  1    28.37     1.0358 27.39 < 2.22e-16 26.34  30.40
#>   0  1    20.74     1.0358 20.03 < 2.22e-16 18.71  22.77
#>   0  0    15.05     0.7911 19.02 < 2.22e-16 13.50  16.60
#> 
#> Prediction type:  response 
#> Columns: type, am, vs, estimate, std.error, statistic, p.value, conf.low, conf.high 
#> 

library(nnet)
nom <- multinom(factor(gear) ~ mpg + am * vs, data = mtcars, trace = FALSE)

# first 5 raw predictions
predictions(nom, type = "probs") |> head()
#> 
#>  Group  Estimate Std. Error         z Pr(>|z|)      2.5 %    97.5 %
#>      3 3.624e-05  2.002e-03   0.01810 0.985561 -3.889e-03 3.961e-03
#>      3 3.624e-05  2.002e-03   0.01810 0.985561 -3.889e-03 3.961e-03
#>      3 9.348e-08  6.912e-06   0.01352 0.989210 -1.345e-05 1.364e-05
#>      3 4.045e-01  1.965e-01   2.05788 0.039602  1.924e-02 7.897e-01
#>      3 1.000e+00  1.246e-03 802.40563  < 2e-16  9.975e-01 1.002e+00
#>      3 5.183e-01  2.898e-01   1.78858 0.073683 -4.967e-02 1.086e+00
#> 
#> Prediction type:  probs 
#> Columns: rowid, type, group, estimate, std.error, statistic, p.value, conf.low, conf.high, mpg, cyl, disp, hp, drat, wt, qsec, vs, am, gear, carb 
#> 

# average predictions
avg_predictions(nom, type = "probs", by = "group")
#> 
#>  Group Estimate Std. Error      z   Pr(>|z|)   2.5 % 97.5 %
#>      3   0.4688    0.04043 11.595 < 2.22e-16 0.38952 0.5480
#>      4   0.3750    0.06142  6.106 1.0231e-09 0.25462 0.4954
#>      5   0.1562    0.04624  3.379  0.0007279 0.06561 0.2469
#> 
#> Prediction type:  probs 
#> Columns: type, group, estimate, std.error, statistic, p.value, conf.low, conf.high 
#> 

by <- data.frame(
    group = c("3", "4", "5"),
    by = c("3,4", "3,4", "5"))

predictions(nom, type = "probs", by = by)
#> 
#>  Estimate Std. Error      z   Pr(>|z|)   2.5 % 97.5 %  By
#>    0.4219    0.02312 18.246 < 2.22e-16 0.37656 0.4672 3,4
#>    0.1562    0.04624  3.379  0.0007279 0.06561 0.2469   5
#> 
#> Prediction type:  probs 
#> Columns: type, estimate, std.error, statistic, p.value, conf.low, conf.high, by 
#> 

# sum of predicted probabilities for combined response levels
mod <- multinom(factor(cyl) ~ mpg + am, data = mtcars, trace = FALSE)
by <- data.frame(
    by = c("4,6", "4,6", "8"),
    group = as.character(c(4, 6, 8)))
predictions(mod, newdata = "mean", byfun = sum, by = by)
#> 
#>  Estimate Std. Error      z   Pr(>|z|)   2.5 % 97.5 %  By
#>   0.91584     0.1218 7.5188 5.5296e-14  0.6771 1.1546 4,6
#>   0.08416     0.1218 0.6909    0.48963 -0.1546 0.3229   8
#> 
#> Prediction type:  probs 
#> Columns: type, estimate, std.error, statistic, p.value, conf.low, conf.high, by 
#>